It's theft at it's finest right there... pay to play get banned boom. Good ol waste of a few hundred bucks and time.

Its not theft. You paid a licensing fee. You also agreed to ToS and EULA. These state that Riot has the ability to terminate your account and revoke your licenses for whatever reason they choose without offering a refund. You also agreed to follow the rules.

Your account was punished because you violated the agreement you accepted. You are not legally in any way deserving of a refund. You can waste your time and money all you want.